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<title>Problem 1653. -- [Usaco2006 Feb]Backward Digit Sums -- 衡阳八中OJ离线版-2012-02-29</title><center><h2>1653: [Usaco2006 Feb]Backward Digit Sums</h2><span class=green>Time Limit: </span>5 Sec&nbsp;&nbsp;<span class=green>Memory Limit: </span>64 MB<br><span class=green>Submit: </span>132&nbsp;&nbsp;<span class=green>Solved: </span>106<br>[<a href='submitpage.php?id=1653'>Submit</a>][<a href='problemstatus.php?id=1653'>Status</a>][<a href='bbs.php?id=1653'>Discuss</a>]</center><h2>Description</h2><div class=content>
FJ and his cows enjoy playing a mental game. They write down the
numbers from 1 to N (1 <= N <= 10) in a certain order and then sum
adjacent numbers to produce a new list with one fewer number.  They
repeat this until only a single number is left.  For example, one
instance of the game (when N=4) might go like this:

    3   1   2   4
      4   3   6
        7   9
         16

Behind FJ's back, the cows have started playing a more difficult
game, in which they try to determine the starting sequence from
only the final total and the number N.  Unfortunately, the game is
a bit above FJ's mental arithmetic capabilities.

Write a program to help FJ play the game and keep up with the cows.

</div><h2>Input</h2><div class=content>* Line 1: Two space-separated integers: N and the final sum.

</div><h2>Output</h2><div class=content>
* Line 1: An ordering of the integers 1..N that leads to the given
        sum.  If there are multiple solutions, choose the one that is
        lexicographically least, i.e., that puts smaller numbers
        first.
</div><h2>Sample Input</h2>
			<div class=content><span class=sampledata><br />
4 16<br />
</span></div><h2>Sample Output</h2>
			<div class=content><span class=sampledata><br />
3 1 2 4<br />
<br />
OUTPUT DETAILS:<br />
<br />
There are other possible sequences, such as 3 2 1 4, but 3 1 2 4<br />
is the lexicographically smallest.<br />
</span></div><h2>HINT</h2>
			<div class=content><p></p></div><h2>Source</h2>
			<div class=content><p><a href='problemset.html?search=Silver'>Silver</a></p></div><center>[<a href='submitpage.php?id=1653'>Submit</a>][<a href='problemstatus.php?id=1653'>Status</a>][<a href='bbs.php?id=1653'>Discuss</a>]</center>﻿<br>

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